﻿Diffusion 
  to 
  Conducting 
  Gases, 
  473 
  

  

  So 
  that 
  equation 
  (1) 
  becomes 
  

  

  rp= 
  2 
  A 
  n 
  sin 
  € 
  ca 
  K 
  \ 
  

  

  The 
  coefficients 
  A„ 
  are 
  determined, 
  as 
  before, 
  by 
  making 
  

   p=p 
  and 
  * 
  = 
  simultaneously, 
  and 
  we 
  have 
  

  

  >n 
  i 
  a 
  

  

  - 
  =Po 
  ] 
  rsu 
  

  

  Jo 
  

  

  ClA 
  n 
  

  

  — 
  =p 
  1 
  rsin 
  t 
  

  

  _ 
  q»(-l)»-» 
  

  

  W7T 
  

  

  Hence 
  

  

  »' 
  Ti- 
  

  

  ft- 
  £ 
  

  

  irnv 
  

  

  and 
  the 
  ratio 
  — 
  becomes 
  in 
  this 
  case 
  

  

  '' 
  n=l 
  n 
  

  

  By 
  means 
  of 
  this 
  equation 
  a 
  rough 
  estimate 
  could 
  be 
  made 
  

  

  of 
  the 
  amount 
  of 
  impurity 
  (A) 
  that 
  would 
  be 
  removed 
  from 
  a 
  

  

  gas 
  (B) 
  by 
  bubbling 
  through 
  a 
  liquid 
  which 
  absorbed 
  the 
  gas 
  A. 
  

  

  o 
  t 
  

  

  The 
  solution 
  shows 
  that 
  — 
  is 
  constant 
  when 
  — 
  9 
  is 
  constant 
  ; 
  

  

  or 
  that 
  in 
  order 
  to 
  reduce 
  the 
  quantity 
  of 
  the 
  gas 
  A 
  by 
  a 
  given 
  

   fraction 
  the 
  time 
  the 
  bubble 
  takes 
  to 
  rise 
  in 
  the 
  liquid 
  must 
  

  

  be 
  proportional 
  to 
  the 
  square 
  of 
  its 
  radius. 
  When 
  — 
  is 
  small, 
  

  

  account 
  need 
  only 
  be 
  taken 
  of 
  the 
  first 
  term, 
  and 
  the 
  value 
  of 
  

  

  — 
  is 
  easily 
  calculated 
  when 
  k 
  is 
  known. 
  

  

  qo 
  

  

  Section 
  II. 
  

  

  4. 
  The 
  number 
  of 
  charged 
  carriers 
  or 
  ions 
  which 
  are 
  present 
  

   in 
  a 
  gas 
  and 
  give 
  rise 
  to 
  conductivity 
  is 
  very 
  small 
  compared 
  

   with 
  the 
  total 
  number 
  of 
  molecules 
  of 
  the 
  gas. 
  These 
  charged 
  

   carriers 
  we 
  will 
  suppose 
  constitute 
  the 
  gas 
  A, 
  and 
  the 
  rest 
  of 
  

   the 
  molecules 
  will 
  be 
  denoted 
  as 
  the 
  gas 
  B. 
  

  

  Let 
  rn 
  be 
  the 
  mass 
  of 
  a 
  carrier 
  ; 
  e 
  its 
  charge 
  ; 
  u, 
  v, 
  to 
  the 
  

   velocities 
  of 
  A 
  parallel 
  to 
  the 
  axes 
  ; 
  p 
  the 
  pressure 
  of 
  A; 
  n 
  the 
  

   number 
  of 
  carriers 
  per 
  cubic 
  centimetre 
  ; 
  X, 
  Y, 
  Z 
  the 
  

   electric 
  forces. 
  

  

  